1 September 2004 Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model A. Introduction and assumptions The classical normal linear regression model can be wri
Chapter 10
Random Regressors and
Moment-Based Estimation
Principles of Econometrics, 4th
Edition
Chapter 10: Random Regressors and
Moment-Based Estimation
Page 1
Chapter Contents
10.1 Linear Regressi
Chapter 9
Regression with Time Series
Data:
Stationary Variables
Walter R. Paczkowski
Rutgers University
Principles of Econometrics, 4th
Edition
Chapter 9: Regression with Time Series Data:
Stationary
Regression Motivation
Dan Yavorsky
1/12
Plan
I want to show you something that is mathematically more general
than what is done in class.
But then I will tie the general things specifically to linear
IV. Introduction to Time Series AR(1) Model and Forecasting
a.
b.
c.
d.
e.
f.
g.
Introduction to Dependent Observations
Checking for Independence
Autocorrelation
The AR(1) Model
Random Walks
Trend Mod
II. The Multiple Regression Model
a.
b.
c.
d.
e.
f.
g.
The Multiple Regression Model
The Data and Least Squares
Inference and F-tests
Prediction
Multiple Regression Explained: The Pricing Example
More
V. Advanced Regression Topics
a.
b.
c.
d.
e.
f.
g.
h.
MR Standard Errors
Multi-colinearity
Standardized Residuals, Leverage, and Outliers
Nonlinearity
Dummy Variables
Heteroskedasticity
Bootstrapping
VI. Likelihood and Maximum Likelihood Estimation
a.
b.
c.
d.
e.
The Likelihood Function for Regression Models
Method of Maximum Likelihood
Properties of MLEs
ARCH-M Likelihood and Example
Conclusions
Relaxing OLS Assumptions
Dan Yavorsky
1/13
Regression
In general regression tries to explain Y with X:
Y = f (X) +
Very often, X is assumed to be linear in the parameters :
Y = f (X) +
In Linear Reg
Key Statistical and Mathematical Prerequisites
NOTE TO THE STUDENT:
This document is designed to review previously acquired statistics knowledge. It is not
designed to teach this material from scratch
Tutorial: ggplot2
Ramon Saccilotto
Universittsspital Basel
Hebelstrasse 10
T 061 265 34 07 F 061 265 31 09 [email protected]
www.ceb-institute.org
Basel Institute for Clinical Epidemiology and Biost
Introduction to Rossis 237Q Slides
I have made this longer than usual, because I lack the time to make it
short. - Pascal
I had the time!
A lot of work has gone into simplifying and stripping down to
Name: Vanessa Ee Shan, Wong
ID: 260736328
6.7
a) The proposed research is too limited. There are other factors that contribute to salaries. For
instance, education level. The gender with the lower wag
Chapter 4
Prediction, Goodness-of-fit, and
Modeling Issues
Walter R. Paczkowski
Rutgers University
Principles of Econometrics, 4th
Edition
Chapter 4: Prediction, Goodness-of-fit, and Modeling Issues
P
Chapter 7
Using Indicator Variables
Walter R. Paczkowski
Rutgers University
Principles of Econometrics, 4th
Edition
Chapter 7: Using Indicator Variables
Page 1
Chapter Contents
7.1 Indicator Variable
Chapter 8
Heteroskedasticity
Walter R. Paczkowski
Rutgers University
Principles of Econometrics, 4th
Edition
Chapter 8: Heteroskedasticity
Page 1
Chapter Contents
8.1 The Nature of Heteroskedasticity
Economics 671 Problem Set #4 Convergence Concepts
2 (1) Suppose that Xn a for some constant a and consider the sequence Yn = Xn . Show directly
p
[that is, without making use of the theorem discussed
Economics 671 Solutions: Problem Set #2 Special Distributions and Changes of Variable
(1) MATLAB code for this portion of the problem set has been provided. Note that the inverse transform method sugg
Economics 573 Problem Set 5 Fall 2002 Due: 4 October 2002 1. In random sampling from any population with E(X) = : and Var(X) = F2, show (using Chebyshev's inequality) that sample mean converges in pro
Economics 573 Problem Set 4 Fall 2002 Due: 20 September 1. Ten students selected at random have the following "final averages" in physics and economics. Students Physics Economics a. 1 66 75 2 70 70 3
Economics 671 Problem Set #1 Univariate Probability
(1) Casella and Berger, 2.24: Compute E(x) and Var(X) for each of the following probability distributions (a) f (x) = axa-1 , 0 < x < 1, a > 0.
1 (b
Economics 671 Solutions: Problem Set #4 Convergence Concepts
(1) Fix
> 0. We seek to show that
n 2 lim Pr |Xn - a2 | >
= 0.
Choose a > 0 such that 2 + 2|a| <
2 Pr |Xn - a2 | >
and write the above prob
Economics 671 Solutions: Problem Set #2 Multivariate and Conditional Probability
(1) (a) First, note that the density is always positive over its support. Moreover,
0 x
2 exp[(x + y)]dydx = 1
(which
Economics 671 Problem Set #3 Special Distributions and Changes of Variable
(1a) Suppose that f (x) = 2x, 0 x 1.
Describe how you can generate draws from this distribution. (1b) Using MATLAB and your s
Economics 671 Problem Set #5 Central Limit Theorem
(1) Suppose that X1 , X2 , , Xn denote an iid sample from an exponential distribution with density function: f (Xi ) = 1 exp(xi 1 ), xi 0 i. (1a) Usi
Economics 671
Problem Set #2
Multivariate and Conditional Probability
(1) Consider the joint density function
f (x, y) =
2 exp([x + y])
0
for 0 x y, 0 y
otherwise .
(a) Show that this is a valid bivar
University of New Mexico
Economics Department
ECON-309 Introduction to Statistics and Econometrics
Assignment 2
Instructions: This assignment is due on Friday, September 9th. You may submit through Le
Newey-West Standard Errors
To obtain Newey-West autocorrelation-adjusted standard errors requires some work.
Instead of using proc reg, were going to use GMM. Heres the code via an example:
proc model